What is the derivative of y=6^{-4x} ?

The derivative of y=6^{-4x} is -ln(6)*81^{-x}*2^{-4x+2}

What is the first derivative of y=6^{-4x} ?

The first derivative of y=6^{-4x} is -ln(6)*81^{-x}*2^{-4x+2}

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derivative of

y = 6^{- 4 x}

- ln (6) \cdot 8 1^{- x} \cdot 2^{- 4 x + 2}

Solution steps

\frac{d}{d x} (6^{- 4 x})

Simplify

6^{- 4 x} : 129 6^{- x}

= \frac{d}{d x} (129 6^{- x})

Apply exponent rule:

a^{b} = e^{b l n (a)}

129 6^{- x} = e^{(- x) l n (1296)}

= \frac{d}{d x} (e^{(- x) l n (1296)})

Apply the chain rule:

e^{(- x) l n (1296)} \frac{d}{d x} ((- x) ln (1296))

= e^{(- x) l n (1296)} \frac{d}{d x} ((- x) ln (1296))

\frac{d}{d x} ((- x) ln (1296)) = - 4 ln (6)

= e^{(- x) l n (1296)} (- 4 ln (6))

Simplify

e^{(- x) l n (1296)} (- 4 ln (6)) : - ln (6) \cdot 8 1^{- x} \cdot 2^{- 4 x + 2}

= - ln (6) \cdot 8 1^{- x} \cdot 2^{- 4 x + 2}

What is the derivative of y=6^{-4x} ?
The derivative of y=6^{-4x} is -ln(6)*81^{-x}*2^{-4x+2}
What is the first derivative of y=6^{-4x} ?
The first derivative of y=6^{-4x} is -ln(6)*81^{-x}*2^{-4x+2}